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20 May 2011, 17:07

Your option cannot form a triangle and second option makes the parallelogram a Square (questions says Rectangular region). So neither of them is sufficient enough to justify your answer.
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Your option cannot form a triangle and second option makes the parallelogram a Square (questions says Rectangular region). So neither of them is sufficient enough to justify your answer.

I meant to say; any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5.

one side: \(2\sqrt{6}\) and other side: \(1\); hypotenuse: \(5\)

\(1^2+(2\sqrt{6})^2=5^2\)

And a square is a specialized rectangle in GMAT.

Hi ,Your statement "any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5. " is not true if its a right angle traingle with diagonal as 5. as per Pythagoras theorem other 2 sides should be 3 and 4 so A is sufficient alonePl clarify incase I am missing anything

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Your option cannot form a triangle and second option makes the parallelogram a Square (questions says Rectangular region). So neither of them is sufficient enough to justify your answer.

I meant to say; any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5.

one side: \(2\sqrt{6}\) and other side: \(1\); hypotenuse: \(5\)

\(1^2+(2\sqrt{6})^2=5^2\)

And a square is a specialized rectangle in GMAT.

Hi ,Your statement "any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5. " is not true if its a right angle traingle with diagonal as 5. as per Pythagoras theorem other 2 sides should be 3 and 4 so A is sufficient alonePl clarify incase I am missing anything

Pythagoras theorem says ..Hyp^2 = sum of the squares of other 2 sides..it never said the all the sides are phythagoras triplets like 3,4,5 and 9,12,15so if the hyp = 5, yes its easier to assume that other 2 sides follow the triplet format and are 3 and 4but nothing stops us from assuming that they can be 1 and 2 sqrt 6.

Show Tags

Your option cannot form a triangle and second option makes the parallelogram a Square (questions says Rectangular region). So neither of them is sufficient enough to justify your answer.

I meant to say; any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5.

one side: \(2\sqrt{6}\) and other side: \(1\); hypotenuse: \(5\)

\(1^2+(2\sqrt{6})^2=5^2\)

And a square is a specialized rectangle in GMAT.

Hi ,Your statement "any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5. " is not true if its a right angle traingle with diagonal as 5. as per Pythagoras theorem other 2 sides should be 3 and 4 so A is sufficient alonePl clarify incase I am missing anything

3,4,5 is just one of the infinite possibilities.

Why don't you draw it and see it yourself.

Draw a horizontal line-segment(AB) of 1 unit . Draw a perpendicular ray directly upward from point A. Now, using divider pointing at point B, and setting the divider to 5 units, make a small arc so that it cuts the ray at some point, say C. Join BC. You now have a right triangle with hypotenuse 5, one side 1 unit, and another side \(\sqrt{5^2-1} = \sqrt{24}= 2 \sqrt{6} \approx 4.9\)

Like this, we have infinite possibilities because there are infinite real numbers between 0 and 5, exclusive.
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